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Corrections to the Text
May 4, 2005
Included below are a list of typos in the text, Signals and Systems, by Alan V. Oppenheim and Alan S. Willsky. The current version of the text is the ninth printing of the second edition. Corrections made prior to the third printing are not listed here. If you find more typos or errors, please e-mail the Head TA ([email protected]). Further corrections will be included as they become available.
◦ On page 20, Equation 1.39 is missing a t in the second exponential. It should be read x(t) = ej^2.^5 t^ (e−j^0.^5 t^ + ej^0.^5 t). ◦ On page 44 in the first paragraph right after 1.6.1, he first sentence should be read: A system is said to be memoryless if its output for each value of the independent variable at a given time is dependent only on the input at that same time. ◦ On page 46 in the paragraph at the bottom, the first sentence should be read: A system is causal if the output at any time depends only on values of the input at the present time and in the past. ◦ On page 56 in Figure 1.48, y 0 [n] in the caption should be replaced with y 0 (t).
◦ On page 87, Figure 2.9(d) has the fourth nonzero impulse labeled on the time scale as “n”. Instead the last nonzero impulse, the seventh one should be labeled “n”. ◦ In Problem 2.45(a-(iii)) on page 151, Figure P2.45 should be modified so that the output of the system is z(t) = y′(t) and not y(t). ◦ In Problem 2.45(d) on page 151, Equation (P2.45-1) should be
y(t) =
∫ (^) ∞
−∞
x′(τ )s(t − τ )dτ.
◦ On page 191 in the paragraph below Equation (3.39), the word funda- mental is misspelled. ◦ On page 206 in Table 3.1, the frequency shifting property for a periodic signal should be
ejM ω^0 tx(t) = ejM^ (2π/T^ )tx(t).
◦ The limits of integration of Property 4 of Problem 3.41 should be changed so that the property is ∫ (^2)
1
x(t) dt = 2
◦ In Figure 5.14 on page 378, the bottom right figure should have the title X(3) (ejω) = X (ej^3 ω). ◦ In Figure 5.17(a) on page 384, the ideal lowpass filter should have cutoff frequencies −ωc and ωc, not −ω 0 and ω 0. ◦ On page 392 in Table 5.2 the top left time domain signal should be changed to: (^) ∑
k=
akejk(2π/N^ )n
instead of the expression in the book. ◦ On page 396, Table 5.3 should be corrected in two places. For continuous time, the Fourier Transform/Frequency domain block should have the following,
X(jω) =
∫ (^) ∞
−∞
x(t)e−jωtdt,
instead of what is written for X(jω). For discrete time, the Fourier Transform/Time domain block should have the following,
x[n] =
2 π
∫
2 π
X
( ejω
) ejωndω
instead of what is written for x[n].
◦ In Problem 7.30 on page 567, Figure P7.30 has two extraneous parts. The equations
dyc(t) dt
- yc(t) = xc(t) and y[n] = yc(nT ) may be re- moved.
◦ In Figure 8.21 on pgae 600, the magnitude bars around H(jω) are so faint that they are almost invisible. ◦ In Figure 8.23 on page 602, the amplitude of the signal c(t) should be labeled with the value 1.
◦ On page 686, in the discussion on the time scaling property for Laplace Transforms, the first sentence after formula (9.90) should read, That is, for any value s in R [which is illustrated in figure 9.24(a)], the value a · s will be in R 1 ,... Also, in Figure 9.24 (b and c), the boundaries of the region of conver- gence should be a · r 2 and a · r 1 , (rather than r 2 /a and r 1 /a). ◦ On page 691, the bottom equation of Equation (9.5.10) in Table 9. should be lim t→∞ x(t) = lim s→ 0 sX(s)
◦ In Problem 11.45(c) on page 889, the last line should read, ”Consider both the case 0 < a < 2 and the case a > 2.” ◦ In Problem 11.32(c), it should say, “let p(s) denote the greatest common factor of N 1 (s) and D 2 (s).”
◦ On page 933, the answer for Problem 3.1 should be: 4 cos
( π 4 t
) −8 cos
( 3 π 4 t^ +^
π 2
) .
